Basically the answer to your question is the Nicene Creed, but you have a collection of assumptions that are directly opposed to the reasoning of scripture.
First the Sonship of Christ:
We believe in one Lord, Jesus Christ,
the only Son of God,
eternally begotten of the Father,
God from God, light from light,
true God from true God,
begotten, not made,
of one Being with the Father;
through him all things were made.
For us and for our salvation
he came down from heaven,
was incarnate of the Holy Spirit and the Virgin Mary
and became truly human.
For our sake he was crucified under Pontius Pilate;
he suffered death and was buried.
On the third day he rose again
in accordance with the Scriptures;
he ascended into heaven
and is seated at the right hand of the Father.
He will come again in glory to judge the living and the dead,
and his kingdom will have no end. (Nicene Creed)
This means that the Son of God is an eternal being who was loved by the Father before the creation, everything that happened in time is secondary to his role of Son. Therefore, to compare him to anyone else is like comparing infinite to finite, i.e. everything else is nothing to God comparatively. He can't love them in any way like he loves his only Son.
Love of God is spiritual and not like you imagine. The essential 'nature of God' is goodness and love, which means a love of that which is most excellent, i.e. himself. Everything God ultimately loves is within himself, for he alone is excellent beyond all measure. This is also why the only command is to love Him, which will manifest itself in love of our neighbor for his sake. His love for us is just an outworking of his higher love of Himself, being the only object deserving of devotion.
Your question smacks into the face of these primary building blocks of God's revelation of himself. First you very incorrectly assume 'we are all God's children'. The bible say's that nowhere, rather, as a good example taylor made for this question, Christ said in response to some Jews that said they were 'God's children':
Jesus said to them, “If God were your Father, you would love me, for I have come here from God. I have not come on my own; God sent me. Why is my language not clear to you? Because you are unable to hear what I say. You belong to your father, the devil, and you want to carry out your father’s desires. He was a murderer from the beginning, not holding to the truth, for there is no truth in him. When he lies, he speaks his native language, for he is a liar and the father of lies. (John 8:42-44, NIV)
This verse really ties both subjects you have so aptly confused together in your question. For first, Jesus shows how he is the 'only Son', for he came from before time began, from the Father in heaven, humbling himself into a human nature, but they were unable to comprehend him. They just knew how to babble about their own view of themselves as being God's children. They were not aware that not everyone is God's child, only those adopted as a children through the death and merits of Christ's death and resserected life - are sons.
So now about his love. While you and I stood blaspheming God, boasting of our selves, yet fully deserving of his eternal anger, while fools, while wicked, while stubborn, while unteachable, while full of jealousy, anger, lust and every other filth, -- while we were in this state, and this alone, did God sent his only Son to die for us. One really must use the word 'I' to understand it. God sent his holy eternal Son to leave the glory of heaven, to suffer into the inexpressibly lower life of a human, let alone an infant in swaddling clothes, to live among sinners, all in order to save 'me' or in this case, 'you'. He took 'your' endless perverse and foolish thoughts, your monstrous evil deeds, and all things from your life unworthy of the eternal being and smashed his own eternally beloved Son into death for your immeasurable wretchedness. Then he counted up all the righteousness that Christ lived in the flesh under all his holy Laws for man, and collected them all into a 'perfect righteousness' and hammered that absolute perfection onto 'you' (I am using a future sense on your behalf) - making you perfect under his holy eyes, while yet never yet ever doing anything good.
So, how is it that God loves sinners? He suffered to watch his dear beloved eternal Son, who he has infinite filial and Fatherly emotions towards (which is neither comprehensible nor explained by scripture yet declared to be true and accepted by all Christians)- he suffered that 'one and only' to pay for your eternal offense to all that is good and praiseworthy. Not only so but to declare you righteous as a gift, with nothing required of you accept receiving that love by faith, you are granted tamper-proof eternally life, which no man, devil, or sin can steel away.
Obviously the assumptions of scripture, what is declares to be obvious and what it declares to be nonsense is basically an inversion your question. In other words the scripture forcefully opposes you and it also opposes me in equal manner whenever I ponder my own foolish thoughts that are not worthy of his majesty and care. This is really a matter of life, wisdom, knowledge, and glory, verses death, folly, ignorance and sin. It really about choosing faith in God, or following the Devil, at least from the view ported to us in the Bible. It always calls for a decided response.